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Let K be differential field with algebraically closed field of constants. LetK^diff be a differential closure of K, and L the (iterated) Picard-Vessiotclosure of K inside K^diff. Let G be a linear differential algebraic group overK and X a differential algebraic torsor for G over K. We prove that X(L) isKolchin-dense in X. When G is finite-dimensional we prove that X(L) =X(K^diff). We give close relationships between Picard-Vessiot extensions of Kand torsors for suitable finite-dimensional linear differential algebraicgroups over K. We suggest some differential field analogues of the notion ofboundedness for fields (Serre's property F).

Picard-Vessiot extensions, linear differential algebraic groups and their torsors